I would like to know whether FLASH AS3 has some option to get all the files names from a folder specified and show it in a dynamic text box? Whenever some new files added to this folder it should update the list accordingly.

Not particularly experienced in this field myself, but I've found its just easier to implement an XML file which lists the contents of the folder. It just means that when you upload a new file you have to add it to the list in the xml file also. No real hardship once you figure out the mechanics of it

Yes, if you're going to be on a web page and listing server files, then you'd need some server-side code, like php or .net, to send the list to your app. If you are making something standalone to work on the users machine, then you'd need to use AIR and its File class.